Ideas on how to make a neural net learn how to split sequence into sub sequences
The problem in the original question is akin to that of inducing a context-sensitive grammar (CSL), except that it is harder because a CSL is assumed to be composed of fixed-length subsequences. It is probably closer to the problem of inducing a Reber grammar, but that in turn seems like an overkill.

LSTMs are known to be able to learn both CSL and Reber grammars. However, I doubt that this is what you really need because of the following comment:


  [...] given an entire book where there is NO spaces anywhere, only characters (including special characters, like commas), in what way can we make the network learn the 'word boudaries' of this book.


This is called morphology induction, and it is a much harder problem than that of simple Reber grammar induction. Note that finding word boundaries is a special case of the problem of finding morpheme boundaries. There have been many attempts to solve this (also see this survey paper for more details and references). 

Most approaches developed seem to rely on statistical principles (like MDL) and do not use neural networks (a counterexample using LSTMs). My intuition is that the extreme morphological variability across languages (ranging from Finno-Ugric languages with highly inflectional morphology to Sino-Tibetan languages with hardly any morphology at all) makes it hard to train neural networks in a language-agnostic way. However, you might have better luck if you focus on a single language.

Hope that helps.